In case you are looking for a user-friendly program that handles binary and ordinal data in factor analysis with ease, Mplus does the job very well in my opinion. That being said, having over 400 items seems like a bit much, even with 2000 subjects.

Are you saying you want a program that does IRT (also called latent trait modeling)? This is a latent variable model for binary items, and is common in education where you often have a large number of binary items. See https://www.jstatsoft.org/article/view/v048i06 for details.

This question was on ResearchGate:

https://www.researchgate.net/post/How_to_test_factor_analysis_binary_data_in_SPSS

See also:

Article An SPSS R-menu for ordinal factor analysis

and:

https://groups.google.com/g/comp.soft-sys.stat.spss/c/JqNpN07b--c?pli=1

Hello Jacques,

As you say you can use R or Stata.

You also have two free program options (without payment) that allow you to use polychoric correlations as well as do exploratory factor analysis.

The first is JASP (https://jasp-stats.org/download/) with the spss database you can use it, its interface is very simple and quick to use (quite similar to SPSS).

The second is FACTOR (https://psico.fcep.urv.cat/utilitats/factor/Download.html) although its interface is simple, on its website they give you the step by step to load the databases (it is very intuitive and fast to use even if it seems complicated).

Thank you Luis I will try JASP.

As far as I know JASP still does do binary factor analysis (i.e., IRT), see https://github.com/jasp-stats/jasp-issues/issues/160. Maybe this has changed since this was posted. SInce Luis Rodríguez Chávez is suggesting JASP I assume it is. Can you confirm this?

You are right Daniel Wright. JASP can be used. There is an option for polychoric/tetrachoric correlation matrix in JASP but the program do not seem to take the kind of items I have which are True or False type, so a nominal scale. After many trials, it seems JASP only accepts ordinal or scale variables but not nominal types of variables.